The irony in “The Chaser” is that the young man comes looking for a love potion, but will be looking for a death potion later.
Irony is when something unexpected happens. In this story, the title is ironic. At the end of the story, the old man says, "Au revoir," which means he thinks he will be seeing Alan again.
At the end of the story, the old man implies that he sells the love potion for one dollar because people buy it when they are young and naïve, but later in life they will buy the potion that kills the person they once wanted to fall in love with them, for five thousand dollars.
"I like to oblige," said the old man. "Then customers come back, later in life, when they are better off, and want more expensive things. Here you are. You will find it very effective." (p. 3)
A chaser is “a drink drunk after another of a different kind” (freedictionary.com). The title of the story is ironic because it implies that the young man is going to return for the chaser eventually. He will get the woman to fall in love with him, but someday he will not be able to stand it and he will come back to get the potion to kill her.